Title reference. Peter, Joe, Cleveland and Quagmire watch a bootleg copy of the film. Also, the climatic boxing match between Peter and Vladimir Putin is a spoof of the climatic fight between Rocky and Ivan Drago.
After Vladimir Putin calls Peter "chicken", Peter responds "nobody calls me chicken" and challenges him to a fight, just as Marty McFly does in the "Back to the Future" sequels.
After Vladimir Putin calls Peter "chicken", Peter responds "nobody calls me chicken" and challenges him to a fight, just as Marty McFly does in the "Back to the Future" sequels.